A technique controls operation of a local application running on a user device (e.g., a smart phone, a tablet, a personal digital assistant, etc.). The technique involves receiving, by the user device, mouse input from external electronic equipment communicating with the user device. The user device has a touchscreen that displays a touchscreen image of the local application. The mouse input indicates user operation of a hardware mouse. The technique further involves translating, by the user device, the mouse input into translated touchscreen input. The technique further involves providing, by the user device, the translated touchscreen input to the local application running on the user device to operate the local application.